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Sibirskii Matematicheskii Zhurnal, 2001, Volume 42, Number 4, Pages 749–770 (Mi smj1423)  

This article is cited in 9 scientific papers (total in 10 papers)

Numerical determination of a canonical form of a symplectic matrix

S. K. Godunova, M. Sadkaneb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Université de Bretagne Occidentale, Département de Mathématiques, 6, Av. Le Gorgeu. BP 809. 29285 Brest Cedex, France
Abstract: We propose an algorithm that transforms a real symplectic matrix with a stable structure to a block diagonal form composed of three main blocks. The two extreme blocks of the same size are associated respectively with the eigenvalues outside and inside the unit circle. Moreover, these eigenvalues are symmetric with respect to the unit circle. The central block is in turn composed of several diagonal blocks whose eigenvalues are on the unit circle and satisfy a modification of the Krein–Gelfand–Lidskii criterion. The proposed algorithm also gives a qualitative criterion for structural stability.
Received: 01.11.2000
English version:
Siberian Mathematical Journal, 2001, Volume 42, Issue 4, Pages 629–647
DOI: https://doi.org/10.1023/A:1010485128908
Bibliographic databases:
UDC: 517.926.7+519.614.4
Language: Russian
Citation: S. K. Godunov, M. Sadkane, “Numerical determination of a canonical form of a symplectic matrix”, Sibirsk. Mat. Zh., 42:4 (2001), 749–770; Siberian Math. J., 42:4 (2001), 629–647
Citation in format AMSBIB
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\by S.~K.~Godunov, M.~Sadkane
\paper Numerical determination of a~canonical form of a~symplectic matrix
\jour Sibirsk. Mat. Zh.
\yr 2001
\vol 42
\issue 4
\pages 749--770
\mathnet{http://mi.mathnet.ru/smj1423}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1865470}
\zmath{https://zbmath.org/?q=an:1071.65049}
\transl
\jour Siberian Math. J.
\yr 2001
\vol 42
\issue 4
\pages 629--647
\crossref{https://doi.org/10.1023/A:1010485128908}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000170501200002}
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  • https://www.mathnet.ru/eng/smj/v42/i4/p749
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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